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Abstract

In this paper, we extend the Hilbert space
embedding approach to handle conditional
distributions. We derive a kernel estimate
for the conditional embedding, and show its
connection to ordinary embeddings. Conditional
embeddings largely extend our ability
to manipulate distributions in Hibert spaces,
and as an example, we derive a nonparametric
method for modeling dynamical systems
where the belief state of the system is
maintained as a conditional embedding. Our
method is very general in terms of both the
domains and the types of distributions that
it can handle, and we demonstrate the effectiveness
of our method in various dynamical
systems. We expect that conditional embeddings
will have wider applications beyond
modeling dynamical systems.